Imaging with rectangular transmission gratings

In a restricted class of imaging that is due to rectangular transmission gratings, the image formation of coarse periodic objects has been considered in the close vicinity of the gratings under incoherent illumination. The imaging occurs at an extremely high demagnification, typically of the order of 10³, and is determined by the ratio of the periods of the pupil grating and the object. Analyses based on geometrical optics, Fresnel–Kirchhoff diffraction theory, and the optical transfer function (OTF) consideration have been given. It is revealed that the frequency response assumesfinite values only at certain allowablespatial frequencies, which are equal to the integral multiples of the pupil grating frequency. The system OTF has been calculated by varying the normalized-image distance α. The incoherent images under Fourier imaging conditions have been explained in terms of the present mathematical formulations.